Question

The town of Tanjung Kota had a population of 15000 . Five years later, the population had increased to 20000 . Assuming that the rate of the population is proportional to the population. a) Find the value of the growth constant, k. Hence, write the exponential model of the population of Tanjung Kota b) Estimate the population after 25 years c) Estimate the doubling time for the town's population?

Answer 1

The growth constant, k, is approximately 0.08093. The estimated population after 25 years is approximately 113,485. The estimated doubling time for the town's population is approximately 8.54 years.

Step-by-step explanation:

To find the growth constant, k, we can use the formula:

k = ln(P2/P1)/t

where P1 is the initial population, P2 is the final population, and t is the time in years. Given that P1 = 15000, P2 = 20000, and t = 5, we can substitute these values into the formula:

k = ln(20000/15000)/5 = ln(4/3)/5

Approximately, k = 0.08093.

The exponential model of the population of Tanjung Kota is therefore given by:

P(t) = P(0)ekt

To estimate the population after 25 years, we substitute t = 25 into the exponential model:

P(25) = 15000 * e0.08093*25 ≈ 15000 * e2.02325 ≈ 15000 * 7.5655622 ≈ 113484.93

Hence, the estimated population after 25 years is approximately 113,485.

To estimate the doubling time for the town's population, we can use the formula:

td = ln(2)/k

By substituting the value of k, we get:

td = ln(2)/0.08093 ≈ 8.54

Hence, the estimated doubling time for the town's population is approximately 8.54 years.

Learn more about Exponential Growth